The Variable-Order Fractional Calculus of Variations

This book intends to deepen the study of the fractional calculus, giving special emphasis to variable-order operators. It is organized in two parts, as follows. In the first part, we review the basic concepts of fractional calculus (Chapter 1) and of the fractional calculus of variations (Chapter 2). In Chapter 1, we start with a brief overview about fractional calculus and an introduction to the theory of some special functions in fractional calculus. Then, we recall several fractional operators (integrals and derivatives) definitions and some properties of the considered fractional derivatives and integrals are introduced. In the end of this chapter, we review integration by parts formulas for different operators. Chapter 2 presents a short introduction to the classical calculus of variations and review different variational problems, like the isoperimetric problems or problems with variable endpoints. In the end of this chapter, we introduce the theory of the fractional calculus of variations and some fractional variational problems with variable-order. In the second part, we systematize some new recent results on variable-order fractional calculus of (Tavares, Almeida and Torres, 2015, 2016, 2017, 2018). In Chapter 3, considering three types of fractional Caputo derivatives of variable-order, we present new approximation formulas for those fractional derivatives and prove upper bound formulas for the errors. In Chapter 4, we introduce the combined Caputo fractional derivative of variable-order and corresponding higher-order operators. Some properties are also given. Then, we prove fractional Euler-Lagrange equations for several types of fractional problems of the calculus of variations, with or without constraints.Comment: The final authenticated version of this preprint is available online as a SpringerBrief in Applied Sciences and Technology at [https://doi.org/10.1007/978-3-319-94006-9]. In this version some typos, detected by the authors while reading the galley proofs, were corrected, SpringerBriefs in Applied Sciences and Technology, Springer, Cham, 201

Diffusion-limited deposition with dipolar interactions: fractal dimension and multifractal structure

Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation function at a given height, the mean height of the upper surface for a given number of deposited particles and the interfacial width at a given height. Evidences are given that the fractal dimension of the deposits remains constant as the deposition proceeds, independently of the dipolar strength. These same deposits are used to obtain the growth probability measure through Monte Carlo techniques. It is found that the distribution of growth probabilities obeys multifractal scaling, i.e. it can be analyzed in terms of its $f(\alpha)$ multifractal spectrum. For low dipolar strengths, the $f(\alpha)$ spectrum is similar to that of diffusion-limited aggregation. Our results suggest that for increasing dipolar strength both the minimal local growth exponent $\alpha_{min}$ and the information dimension $D_1$ decrease, while the fractal dimension remains the same.Comment: 10 pages, 7 figure

Diffusion-limited deposition of dipolar particles

Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered deposits. In the dipolar regime, the order and geometry of the clusters depend on the strength of the interactions and the magnetic properties are tunable by controlling the growth conditions. At later stages, the growth is dominated by thermal effects and the diffusion-limited universal regime obtains, at finite temperatures. At low temperatures the crossover size increases exponentially as T decreases and at T=0 only the dipolar regime is observed.Comment: 5 pages, 4 figure

Synthesis of an antibody-like material for the detection of Albumin

6th Graduate Student Symposium on Molecular Imprinting6th Graduate Student Symposium on Molecular Imprinting, Medway School of Pharmacy, Kent, 27-28 de Agosto 2015A novel molecularly imprinted polymer (MIP) is presented for the detection of Albumin, currently a biomarker of several diseases. The material acted as an antibody for Albumin and was obtained through a bulk imprinting approach, by electropolymerizing Eriochrome blackT (EBT) around the target protein

Concentração letal (CL50) do óleo essencial de mentha piperita (lamiaceae) em pirarucus arapaima gigas.

Na piscicultura, diversos produtos fitoterápicos vêm sendo usados no tratamento das parasitoses, principalmente causadas por helmintos. Mentha piperita, planta usada na medicina popular para tratar nauseas, vômitos, indigestão, desordens estomacais, cólicas mestruais e verminoses não tem sido testada em peixes, incluindo pirarucu Arapaima gigas. Porém, é importante conhecer a toxicidade de qualquer produto antes de recomendar a sua concentração terapêutica. Este ensaio realizado no Laboratório de Sanidade de Organismos Aquáticos da Embrapa Amapá, Macapá (AP), teve como objetivo determinar a concentração letal média (CL50-4h) do óleo essencial (OE) de M. piperita para pirarucus. Neste ensaio de toxicidade utilizou-se 168 alevinos de pirarucu (34,7 ± 12,4 g e 16,8 ± 2,0 cm) que após aclimatação foram distribuídos aleatoriamente em 14 tanques com volume para 80 L de água e na densidade de 12 peixes/tanque. O delineamento experimental foi inteiramente casualizado, constituído por dois grupos controles (um somente água do cultivo e outro água do cultivo contendo 80 ?L de álcool etílico absoluto) e seis concentrações (20, 40, 80, 100, 130 e 160 mg/L) de OE de M. piperita em duplicatas. As concentrações do OE foram diluídas em álcool etílico (1g:10 mL). Durante o período de 4 horas de exposição ao OE, os peixes foram mantidos sem alimentação, em sistema estático de água e a CL50-4h, foi calculada usando o método de Trimmed Spearman-Karber. Os resultados mostraram que a CL50-4h de M. piperita foi 38 mg/L, com intervalo de confiança (95%) variando de 30-40 mg/L. Portanto, o teste de toxicidade aguda indica que as concentrações clínicas para banhos terapêuticos de pirarucus com OE de M. piperita devem ser abaixo desses valores obtidos, para evitar mortalidade dos peixes, que é indesejada em qualquer piscicultura durante o tratamento antiparasitário.US100

Ecologia parasitária de Metynnis lippincottianus Cope, 1870 (Serrasalmidae) na Amazônia Oriental, Estado do Amapá, Brasil.

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A novel printed 3-electrode system for the electrochemical detection of sulfadiazine

We thank the financial support of 3C´s – Cellulose and Cork in the Control of antibiotics in aquaculture (PTDC/AAG-TEC/5400/2014 and POCI-01-0145-FEDER-016637), to FEDER, through COMPETE2020, POCI, and FCT (Fundação para a Ciência e a Tecnologia I.P.).info:eu-repo/semantics/publishedVersio

Primeiro estudo sobre protozoários e metazoários parasitando Hemibrycon surinamesis (Characidae).

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